Key results: cos(20)*cos(40)*cos(80) = 1/8. sin(20)sin(40)sin(80) = sqrt(3)/8. These use the technique of multiplying by 2sin(theta) repeatedly and applying double angle formulas. General: product of cos(theta)cos(2theta)...cos(2^(n-1)theta) = sin(2^ntheta)/(2^nsin(theta)).